On the quantitative estimates of the remainder in normal forms
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We consider an analytic Hamiltonian system with three degrees of freedom and having a family of periodic orbits with a transition stability complex instability. We reduce the Hamiltonian to a normal form around a transition periodic orbit and we obtain H = Z^r + R^r. The analysis of the (truncated) normal form, Z^r, allows the description of a Hopf bifurcation of 2D-tori. However, this communication will concentrate on the study of the remainder, R^r and some comparison between the remainder obtained when considering the normal form around an elliptic equilibrium point and around a critical periodic orbit will be made.